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Complete the square for f(x)=x^2-2x-8

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To complete the square for the quadratic function f(x) = x^2 - 2x - 8, we can follow these steps:

1. Group the x^2 and x terms together:

f(x) = (x^2 - 2x) - 8

2. Take half of the coefficient of the x term, square it, and add it inside the parentheses:

f(x) = (x^2 - 2x + 1 - 1) - 8

f(x) = (x^2 - 2x + 1) - 9

3. Simplify the expression inside the parentheses:

f(x) = (x - 1)^2 - 9

Therefore, the function f(x) can be written in vertex form as f(x) = (x - 1)^2 - 9.

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